"But that's not a question for us, we're not members of the Conservative Party.

"That's up to the Conservative Party to decide whether there is someone else who can heal those wounds and take the party in a different direction, which would ensure that the agreement could stay in place."

Speaking to Sky News in his constituency of Larne on Northern Ireland's east coast, Mr Wilson said that the DUP were not going to be "bullied" or "bribed" into supporting a deal that could see Northern Ireland effectively kept in the single market or customs union.

Image:Sammy Wilson said he would 'never' support the sort of backstop being briefed by Brussels

His constituency contains the port of Larne, identified by EU chief Brexit negotiator Michel Barnier as a place where checks on animals and animal products from Great Britain into Northern Ireland could be intensified in order to prevent a hard border with the Republic of Ireland.

Mr Wilson said he would "never" vote for a withdrawal deal containing the sort of backstop proposal briefed by Mr Barnier to DUP leader Arlene Foster in Brussels this week.

He added that the DUP could vote down the Budget but still support the government in a confidence vote, as long as it changed its approach to Brexit.

Image:Mr Wilson said the DUP could still support Mrs May in a confidence vote

It comes as the deadline looms for a deal between London and Brussels.

Mr Barnier said on Wednesday an agreement was "within reach" of being met by next Wednesday, when EU28 leaders gather for a summit in Brussels.